The product of 0 and anything is $0$, and seems like it would be reasonable to assume that $0! = 0$. I'm perplexed as to why I have to account for this condition in my factorial function (Trying to learn …

Is there a consensus in the mathematical community, or some accepted authority, to determine whether zero should be classified as a natural number? It seems as though formerly $0$ was considered i...

$0^0=999$ would be a contradiction to the power laws, because then $ (0^0)^2 = 999^2 \ne 0^ {0\cdot2} = 999$. The only two values for $0^0$ consistent with the power laws are $0$ and $1$.

Generally the only reason one sees 1/0 as infinity is because some systems (incorrectly) output infinity when given dividing by zero.

For example, $3^0$ equals 3/3, which equals $1$, but $0^0$ "equals" 0/0, which equals any number, which is why it's indeterminate. Also, 0/0 is undefined because of what I just said.

Jan 12, 2015 · In the context of natural numbers and finite combinatorics it is generally safe to adopt a convention that $0^0=1$. Extending this to a complex arithmetic context is fraught with risks, as is …

Nov 17, 2014 · I began by assuming that $\dfrac00$ does equal $1$ and then was eventually able to deduce that, based upon my assumption (which as we know was false) $0=1$. As this is clearly false …

Oct 28, 2019 · That means that 1/0, the multiplicative inverse of 0 does not exist. 0 multiplied by the multiplicative inverse of 0 does not make any sense and is undefined. Therefore both 1/0 and 0/0 are …

Feb 8, 2011 · You can also prove it by moving the space: "0! = 1" $\Leftrightarrow$ "0 != 1", which is computer notation for "0 $\neq$ 1" :-). Then it depends on what you count as "first principles". If we're …

Jul 20, 2010 · Why is any number (other than zero) to the power of zero equal to one? Please include in your answer an explanation of why $0^0$ should be undefined.